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Analytical technique for the determination of solidification rates during the inward freezing of cylinders

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Abstract

An analytical/experimental approach which permits the determination of solidification rates during the inward solidification of cylinders is proposed. The technique is based on a previous analytical solution that treats the generalized problem of solidification of slabs. This solution is modified by a geometric correlation to compensate for the cylindrical geometry. A number of experiments have been carried out with a special experimental set-up, designed to simulate the inward solidification of cylinders in a water-cooled mould. A series of comparisons of experimental results, numerical predictions and calculations furnished by the proposed technique were made, showing good agreement for any case examined.

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Abbreviations

a s :

Thermal diffusivity of solid metal = k s/c s d s (m2 sec−1)

A i :

Internal surface area of the mould (m2)

b s :

Heat diffusivity of solid metal = (k s c s d s 1/2(J m−2 sec−1/2 K−1)

c s :

Specific heat of solid metal (J kg−1 K−1)

d s :

Density of solid metal (kg m−3)

h :

Newtonian heat transfer coefficien (W m−2 K−1)

H :

Latent heat of fusion (J kg−1)

k s :

Thermal conductivity of solid metal (W m−1 K−1)

q :

Heat flux (W m−2)

r :

Radial position (m)

r o :

Radius of cylinder (m)

r f :

Radius of solid/liquid interface (m)

S :

Thickness of solidified metal (m)

S o :

Thickness of metal side adjunct (m)

t :

Solidification time (sec)

T :

Temperature (K)

T i :

Surface temperature (K)

T f :

Freezing temperature of metal (K)

T o :

Temperature of the coolant (K)

T s :

Temperature at any point in the solidified metal (K)

V 1 :

Volume of remaining liquid metal during the solidification (m3)

V s :

Volume of solidified metal (m3)

V T :

Total volume of metal in the mould (m3)

x :

Distance from metal/mould interface (m)

φ :

Dimensionless solidification constant.

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Authors and Affiliations

  1. Faculty of Engineering, State University of Campinas (UNICAMP), Campinas, SP, Brazil

    R. G. Santos & A. Garcia

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  1. R. G. Santos
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  2. A. Garcia
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Santos, R.G., Garcia, A. Analytical technique for the determination of solidification rates during the inward freezing of cylinders. J Mater Sci 18, 3578–3590 (1983). https://doi.org/10.1007/BF00540730

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